\( \left. \begin{array} { l } { ( x - 5 ) ( x - 2 ) } \\ { ( 2 x - 1 ) ( 2 x + 3 ) } \end{array} \right. \)

Simplify the expression by following steps: - step0: Multiply the terms: \(\left(x-5\right)\left(x-2\right)\) - step1: Apply the distributive property: \(x\times x-x\times 2-5x-\left(-5\times 2\right)\) - step2: Multiply the terms: \(x^{2}-2x-5x-\left(-10\right)\) - step3: Remove the parentheses: \(x^{2}-2x-5x+10\) - step4: Subtract the terms: \(x^{2}-7x+10\) Expand the expression \( (2*x - 1)(2*x + 3) \) Simplify the expression by following steps: - step0: Multiply the terms: \(\left(2x-1\right)\left(2x+3\right)\) - step1: Apply the distributive property: \(2x\times 2x+2x\times 3-2x-3\) - step2: Multiply the terms: \(4x^{2}+6x-2x-3\) - step3: Subtract the terms: \(4x^{2}+4x-3\) Let's expand the two expressions step by step. 1. **First Expression: \( (x - 5)(x - 2) \)** To expand this expression, we apply the distributive property (also known as the FOIL method for binomials): \[ (x - 5)(x - 2) = x \cdot x + x \cdot (-2) - 5 \cdot x - 5 \cdot (-2) \] Simplifying this gives: \[ = x^2 - 2x - 5x + 10 = x^2 - 7x + 10 \] So, the expanded form is: \[ x^2 - 7x + 10 \] 2. **Second Expression: \( (2x - 1)(2x + 3) \)** Again, we use the distributive property: \[ (2x - 1)(2x + 3) = 2x \cdot 2x + 2x \cdot 3 - 1 \cdot 2x - 1 \cdot 3 \] Simplifying this gives: \[ = 4x^2 + 6x - 2x - 3 = 4x^2 + 4x - 3 \] So, the expanded form is: \[ 4x^2 + 4x - 3 \] In summary, the expanded forms of the expressions are: - \( (x - 5)(x - 2) = x^2 - 7x + 10 \) - \( (2x - 1)(2x + 3) = 4x^2 + 4x - 3 \)